Fingerprints of Individual Supermassive Black Hole Binaries in Pulsar Timing Arrays

TL;DR

This paper introduces a new method to identify individual supermassive black hole binaries in pulsar timing array data by detecting their unique spatial correlation pattern, improving localization and distinguishing them from stochastic backgrounds.

Contribution

It derives an analytic expression for the binary's spatial correlation pattern and demonstrates its effectiveness in simulations, enhancing detection and localization capabilities.

Findings

Cross-correlations yield high Bayes factors favoring binary models

Improved sky localization by a factor of 11

Fingerprint-based search is robust against noise over phase-coherent methods

Abstract

With evidence for a nanohertz gravitational-wave background now established by Pulsar Timing Arrays, the search focuses on identifying individual supermassive black hole binaries. We show that these binaries produce a distinct spatial correlation pattern across the array, acting as a deterministic analogue to the stochastic Hellings and Downs curve. We derive a closed analytic expression for this single-source overlap reduction function, $\Upsilon_{ab}$, factorizing the signal into a source-dependent amplitude and a purely geometric fingerprint. Using simulated datasets, we demonstrate that this fingerprint breaks the degeneracy between an individual binary and a stochastic background. Including these cross-correlations yields Bayes factors of $ 144$ favoring the continuous-wave model over a stochastic-background model and $\sim 80$ favoring the continuous-wave model over an uncorrelated red-noise model. Furthermore, these new cross-correlations improve sky localization by a factor of $11\times$ over an uncorrelated search. Finally, while coherent matched filtering offers higher theoretical sensitivity, we argue that a cross-correlation-based search for individual binaries provides a robust alternative that hedges against the possibility of overfitting to noise fluctuations by focusing on the evidence for the correlations. The geometric fingerprints we present here rely on stable spatial correlations rather than phase coherence to identify the first nanohertz gravitational-wave sources.